An Analytic Model of Black Hole Evolution and Gamma-Ray Bursts

An analytic model of the evolution of a rotating black hole (BH) is proposed by considering the coexistence of disk accretion with the Blandford-Znajek process. The evolutionary characteristics of the BH are described in terms of three parameters: the BH spin a*, the ratio k of the angular velocity of the magnetic field lines to that of the BH horizon, and the parameter λ indicating the position of the inner edge of the disk. It is shown that the ratio k being a little greater than 0.5 affects the evolutionary characteristics of the BH significantly, and the BH spin increases rather than decreases in its evolutionary process provided that the initial value of the BH spin is located in an appropriate value range determined by the ratio k. Our calculations show that the system of a BH accretion disk with k = 0.6 might provide a much higher output energy in a shorter timescale for gamma-ray bursts than the same system with k = 0.5.